Title | Structure of entropy solutions for multi-dimensional scalar conservation laws. |
Publication Type | Journal Article |
Year of Publication | 2003 |
Authors | De Lellis C., Otto F., Westdickenberg M. |
Journal | Archiv for Rational Mechanics and Analysis |
Volume | 170 |
Pagination | 137–184 |
Publisher | Springer |
Type of Article | scalar |
ISSN | 0003-9527 |
Keywords | BV functions, entropy-entropy flux pair, finite entropy dissipation, geometric classification of blow-ups, shock wave |
Abstract | An entropy solution u of a multi-dimensional scalar conservation law is not necessarily in BV, even if the conservation law is genuinely nonlinear. We show that u nevertheless has the structure of a BV function in the sense that the shock location is codimension-one rectifiable. This result highlights the regularizing effect of genuine nonlinearity in a qualitative way; it is based on the locally finite rate of entropy dissipation. The proof relies on the geometric classification of blow-ups in the framework of the kinetic formulation. |
Notes | Arch. Ration. Mech. Anal. 170 (2003), no. 2, 137–184 |
URL | http://www.springerlink.com/content/572jhd0jllt9wyre/ |
DOI | 10.1007/s00205-003-0270-9 |
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